Academics
Departments and Curriculum

Mathematics


The teaching of mathematics at Holderness is founded on a practice of collaboration that deepens understanding in two ways. First, we believe that working in partnership with others provides an important exercise in articulating mathematical thinking. Our students read or hear new concepts and then discuss this knowledge with their peers—a process that fosters both active and passive learning, as well as accountability. Second, in working collaboratively, our students develop their critical listening skills. As they seek to understand their peer collaborators, they develop openness and flexibility with regard to their mathematical analyses.


Values

Connections: Students are exposed not only to the many connections present within mathematics as a discipline, but also the exciting connections that occur between mathematics, other fields of study, and a variety of possible career paths. Our students use current events, data from websites and companies, and other available sources to apply classroom concepts to real world applications.

Collaboration: Holderness students work in collaborative learning environments so as to deepen their understanding of mathematical concepts, allowing students the opportunity to articulate their own thinking and to develop the listening skills that allow them to enrich their understanding through teamwork.

Technology: Students have the opportunity to learn and review concepts by using flipped classrooms created by teachers, video tutorials, and Smartboard classroom notes. Students are also able to hone problem solving skills by completing online practice problems. Technology, including graphing calculators and specialized software (e.g., Excel and Fathom), are introduced and explored as important tools to be used in the study of mathematics. We recognize that technology is an important tool; however we also believe that core skills and mental math are important.

Develop Independent and Critical Thinking: We build math confidence. We develop a work ethic towards math. Through problem solving techniques, utilization of extra help, nightly homework, and group projects, our students learn to be confident mathematicians who can think creatively. We recognize that we are preparing our students for jobs and a world that is currently unknown to us and to them, and our goal is for them to be curious and able to adapt to difficult problems.



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Mathematics Course Descriptions

  • Algebra 1

    This is a cornerstone course designed to prepare students to investigate and master more complex, but related, concepts studied over the balance of the mathematics curriculum. Students review the language of algebra, real number operations, and approaches used to solve linear equations before engaging in an expanded study of function graphing, linear analysis, methods of solving linear inequalities, and systems of both inequalities and linear equations. Multiplication of polynomials, factoring, and solving quadratic and exponential functions, together with simplification and evaluation of radical expressions, constitute the remainder of the course.

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  • Geometry

    This course covers the fundamental concepts of geometry, with algebra and discrete mathematical topics woven into the curriculum. Topics include reasoning and proof, building blocks of geometric shapes, congruence and similarity, right triangles and trigonometry, transformations of figures and equations, and surface area and volume.

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  • Algebra 2

    In this course, students continue the study of concepts introduced in Algebra I and Geometry. Concepts such as linear functions, linear regression, data analysis, matrices, and systems of equations are introduced as important tools to explore, analyze, and make conjectures as we further develop mathematical problem-solving skills. Using real-world examples, students explore quadratic equations, polynomials, and operations of functions. Students also examine properties, applications, and graphs of absolute value, exponential, logarithmic, power, radical, and trigonometric functions.

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  • Honors Algebra 2

    In this honors course, students continue the study of concepts introduced in Algebra I and Geometry. Concepts such as linear functions, linear regression, data analysis, matrices, and systems of equations are introduced as important tools to explore, analyze, and make conjectures as we further develop mathematical problem-solving skills. Using real-world examples, students explore quadratic equations, polynomials, and operations of functions. Students also examine properties, applications, and graphs of absolute value, exponential, logarithmic, power, radical, and trigonometric functions.

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  • Algebra 2/Precalculus

    This course is offered to advanced students of mathematics, covering topics in Algebra II in the first semester and Precalculus in the second in preparation for taking AP Calculus AB the following year. Major topics include linear equations and inequalities, systems of equations, functions, conics, polynomials, binomial theorem, vectors, polar and spherical coordinates, combinations and permutations, and complex numbers.

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  • Precalculus

    This course offers a more rigorous approach to the study of functions and to the topics needed for calculus. The emphasis of this course is on analysis through formal mathematical notation and the relation of mathematical concepts to real world scenarios. Major topics include linear, exponential, and logarithmic functions; trigonometric functions; polynomials; radical functions; mathematical limits; composition of functions; and inverses of functions.

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  • Honors Precalculus

    This course is designed for students who have completed Honors Algebra 2. Honors Precalculus covers all of the topics studied in the regular pre-calculus course; however, the pace is slightly faster than regular pre-calculus so that the students will be able to cover more trigonometry and topics that will prepare them for AP Calculus. By the end of the class the students will not only be introduced to topics that are vital to understanding Calculus, such as continuity and limits, but they will also be introduced to the derivative through the limit definition.

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  • Calculus

    Calculus begins with a thorough review of standard high school mathematics in preparation for Calculus and the SAT. The class is designed to introduce students to important Calculus topics and to prepare them for college Calculus. The course will cover the conceptual basis of Calculus including the limit definition of the derivative and Riemann Sums. It will also cover in great detail the rules for differentiation and introduce the integral. By the end of the class students will be exposed to the applications of Calculus with Related Rate and Optimization problems.

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  • AP Calculus AB

    AP Calculus is primarily concerned with developing a student’s understanding of the concepts of calculus through the use of the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Students are expected to take the AP exam in May.

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  • AP Calculus BC

    AP Calculus BC is a semester course designed for students who have completed AP Calculus AB. The course is a continuation of Calculus AB and emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The course will cover advanced integration, differential equations, sequences and series, (including Taylor Series and Maclaurin Series), polar functions, and parametric functions. Students are expected to take the AP Calculus BC exam in May.

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  • Linear Algebra

    Linear Algebra is a semester course for students who have completed AP Calculus AB and/or BC. There are widespread applications of Linear Algebra to business, engineering, and higher level mathematics. The main topics covered are systems of linear equations, matrices, Gaussian elimination, Gram-Schmidt orthogonalization, determinants, vector spaces, eigenvalues, and eigenvectors. Students explore a wide range of applications and may use computer software.
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  • Topics in Mathematics

    In this year-long course, students study mathematics in contexts and develop their abilities to problem solve, reason, and communicate.  Real world situations provide the contexts for mathematical investigation.  The topics include but are not limited to: logic, numeration, statistics, financial mathematics, history of mathematics, and functions.

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  • STEM Robotics

    As an introductory course in robotics the students will learn JAVA computer programming as well as problem solving strategies. This course will involve students in the development, building and programming of a Tetrix robot. Working in teams they design, build, program and document their progress. Topics include motor control, gear ratios, torque, friction, sensors, timing, program loops, logic gates, decision-making, timing sequences, propulsion systems and binary number systems. Student designed robots will be programmed to compete in a variety of autonomous and remote controlled challenges.

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  • AP Statistics

    This is the high school equivalent of a one-semester, introductory college statistics course. In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data, with a focus on univariate and bivariate data. Simulations and probability aid students in constructing models for chance phenomena and lead to the study of inference, where students learn to complete confidence intervals and hypotheses tests. Students use technology, such as the Ti calculator, Fathom, and online applets, to strengthen their understanding of statistical concepts. Throughout the year, students apply statistical skills learned in class to analyze data from a variety of sources, including data from our athletic teams, student-generated data, and online sources. The coursework culminate with AP exam in May.

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  • Computer Science

    Python is an accessible programming language whose simple yet powerful structure and easy-to-use development environment allow students to achieve impressive results quickly. Using this programming language, students will learn the basics of Computer Science including variables, conditional statements (if-else), iterations (loops) and the fundamentals of programming design and implementation. We will also utilize Python’s ‘turtle graphics’ module, which allows for two-dimensional designs. Throughout the course, we will discuss the challenges and opportunities related to the explosion of computer use in the modern world.

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  • AP Computer Science

    This year-long course introduces students to computer science with fundamental topics that include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data(algorithms), analysis of potential solutions, and the ethical and social implications of computing. The course emphasizes both object-oriented and imperative problem solving and design. These techniques represent proven approaches for developing solutions that can scale up from small, simple problems to large, complex problems. The course is designed For 11th and 1 zth grade students who have completed Algebra 2 with a grade of B or higher.

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  • Economics

    This semester-long course serves to introduce students to micro- and macro-economic principles in preparation for further work in economics at the college level. The course actively seeks to apply principles of mathematics to the subject, emphasizing how one uses mathematical models to simplify economic theories and analyze economic patterns. Topics covered include decision-making and cost-benefit analysis, opportunity cost, productivity, scarcity, budget deficits and public debt, monetary policy and the Federal Reserve, GDP, inflation, elasticity of demand, competition and market structures, price ceilings and floors, benefits of trade/comparative advantage, foreign currency markets/exchange rates, and personal finance.

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  • AP Macroeconomics

    This semester long course will give students an understanding of the economy as a whole. Students will look at what is happening at a national level. This course allows the student to think more about theory and abstract ideas in economics. Students will learn about the national debt, GDP in different countries, international economics, and an economy’s growth. This course is for 12th graders, who will have taken economics prior, and may be taken by 11th graders, but it is designed to be taken the year before heading to college. All students must complete summer work in advance of the course.

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  • AP Microeconomics

    This semester long course will give the students an understanding of the basic principles of economics based on what consumers and producers do as individuals in an economy. Microeconomics consists of more math concepts for example, using the supply and demand graphs. We will look at specifics in an economy rather than the whole economy. Students will learn the basic concepts of microeconomics, different product markets and how they work, supply and demand, and the role of the government. This course is for 12th graders, who will have taken economics prior, and may be taken by 11th graders, but it is designed to be taken the year before heading to college. All students must complete summer work in advance of the course.

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View Our Curriculum

Faculty

  • Elizabeth Wolf

    Mathematics Department Chair
    (603) 779-5343
    St. Paul's School
    University of Pennsylvania - BA Mathematics
    University of New Hampshire - MST Mathematics
    Bio
  • Joseph Arsenault

    Mathematics Faculty
    (603) 779-5349
    Bio
  • Ian Casey

    Mathematics Faculty
    Buckingham Browne and Nichols School
    Wheaton College - B.A. Mathematics
    Bio
  • Leigh Anne Connors

    Mathematics Faculty
    (603) 779-5348
    Northwood School
    Plymouth State University - Mathematics
    Bio
  • John Donovan

    Mathematics Faculty
    (603) 779-5321
    SUNY (Buffalo) - PhD
    Hartwick College (NY) - BA
    Harborfields High School
    Harborfields High School
    Hartwick College (NY) - BA
    SUNY Buffalo - PhD
    Bio
  • Richard Eccleston

    Mathematics Faculty & Director of Athletics
    (603) 779-5371
    Holderness School
    Hobart College - BA
    Bio
  • Duane Ford

    Director of Job Programs
    (603) 779-5300
    Middlebury College (VT) - BA
    Holderness School (NH)
    Columbia University (NY) - MA
  • Jay Kourkoulis

    French & Mathematics Faculty
    Bio
  • Jeff Nielson

    Mathematics Faculty
  • Ethan Pfenninger

    Mathematics & Science Faculty
    Bio
  • Victoria Stigum

    Mathematics Faculty
    (603) 779-5312
    Lafayette College (PA) - BA
    Choate Rosemary Hall
    University of New Hampshire - M.B.A.
    Bio
Holderness School
33 Chapel Lane, Holderness NH, 03245
mail P.O Box 1879 Plymouth, NH 03264-1879
phone (603) 536-1257